Prove that for any real numbers

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Prove that for any real numbers a, b, ca,\,b,\,c, sin⁡a+sin⁡b+sin⁡c−sin⁡(a+b+c)=4sin⁡a+b2 sin⁡b+c2 sin⁡c+a2.\sin a+\sin b+\sin c-\sin(a+b+c)=4\sin\frac{a+b}{2}\,\sin\frac{b+c}{2}\,\sin\frac{c+a}{2}.

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